260 DOC.
21
THEORY OF RELATIVITY
[21]
II. The General
Theory
of
Relativity
The
special theory
of
relativity
is
based
on
the fundamental idea that certain
coordinate
systems (inertial systems)
are
equivalent
for the
formulation
of
physical
laws;
these
are
those coordinate
systems
with
respect
to
which the law of inertia and
the law of
constancy
of the
velocity
of
light
in
vacuum
claim
validity.
Are these
systems
indeed
privileged
in
nature,
or
does
this
privileged status stem
from
an
incomplete understanding
of the laws of nature? To be
sure,
according
to
Galileo's
law of
inertia,
the inertial
systems
seem
to
be
privileged
over
coordinate
systems
that
move
in
a
different
manner.
But
the law of
inertia has
a
serious
deficiency
that makes
the
cogency
of this
argument
appear
doubtful.
Let
us imagine a portion
of
space
that
is
entirely
force-free
in
the
sense
of
classical
mechanics, thus,
a
space
from which
gravitating
masses are
far removed.
Then,
according
to mechanics,
there exists
an
inertial
system
K,
with
respect
to
which
a mass
M that
is
left to itself
moves
rectilinearly
and
uniformly through
the
portion
of
space
under consideration. If
one now
introduces
a
coordinate
system
K'
that
is
uniformly
accelerated with
respect
to
K,
then the
mass
M,
which
is
left
to itself,
does
not
move
in
a straight
line with
respect
to
K'
but, rather,
along
a
parabola,
akin
to
the
way
in which
a mass near
the surface of the earth
moves,
relative
to
it,
under the
influence of
gravity.
Can
one
draw from this the conclusion that K'
is
(absolutely)
accelerated? This
conclusion would
not
be
justified.
One
can
just as
well
view K'
as
being
"at rest"
provided
that
one assumes
the
presence,
with
respect
to K',
of
a
uniform
gravitational
field,
which
is
seen as
the
reason
why
the bodies
move
in
an
accelerated fashion with
respect
to
K'.
To be
sure, it
could be
argued against
such
a
conception
that
one
cannot
indicate
the
masses
that
create
this
gravitational
field. But without
violating
the fundamental
principles
of Newtonian
mechanics,
one can imagine
that these
masses are
practically
infinitely
distant.
Besides,
we
do
not
know
to
what
degree
of
exactness
the
Newtonian
law of
gravitation corresponds
to
the
truth.
There
is
one
circumstance that
speaks forcefully
for
our
conception.
All
masses
fall with the
same
acceleration with
respect
to K'
independently
of their
particular
physical
and chemical
nature.
Experience
shows that the
same
holds
true, indeed,
with
extraordinary accuracy,
with
respect
to
the
gravitational
field.
In
light
of
the
remarkable fact that
we
recognize
in
the
gravitational
field
a physical
state
of
space
that
brings
about the
same
behavior of bodies
as
that which obtains with
respect
to
K',
the
hypothesis seems
completely
natural
that,
with
respect
to
K',
there exists
a
gravitational
field that
is
essentially
identical
to
the
gravitational
fields
generated by
masses
according
to
Newton's
law.